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Telford Junior School

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Problem-solving and Reasoning


Problem-solving is the essence of being a mathematician and involves:

  • seeking solutions
  • exploring patterns
  • formulating conjectures

As part of our Mathematics curriculum, the children will have opportunities to learn, develop and use their problem-solving skills in different contexts. They will be exposed to both ROUTINE and NON-ROUTINE problems.


ROUTINE problems are ones where children recall or reproduce facts and methods to help them find the solution. FLUENCY is key for children to be able to solve routine problems efficiently.


NON-ROUTINE problems typically do not have an immediately apparent strategy for solving them and often can be solved in multiple ways. When solving these problems, children need to use their knowledge in a different way. They will make predictions; discuss with others; look for patterns; develop logical and systematic ways of working and explain and prove their findings.


We hope that by working on these types of problems children develop a positive attitude and curiosity about Maths .



Reasoning is the process of applying logical and critical thinking to a mathematical problem in order to work out the correct strategy to use in reaching a solution.


Children need a deep knowledge of facts and concepts (fluency) and need to be able to apply them to a range of contexts. Reasoning helps to bridge the gap between fluency and problem-solving.


We help the children to develop their reasoning skills by:

  • teaching them the mathematical vocabulary they need
  • giving them opportunities to work with others
  • encouraging and helping them to explain their thinking both orally and in writing
  • asking a range of questions to help children move on in their thinking
  • providing reasoning tasks across the mathematics curriculum


We use a range of published, on-line and teacher-made resources to support our teaching of Problem-solving and Reasoning.